Dear Experts
English is not my first language, so I am sorry for any mistakes i make. 
I am 30 y.o. woman and should really know better then to let such questions pop into my head, but i cannot shake off this worry. Here is what happened:

As I was preparing lunch, i opened a can of tuna and sliced my finger, but did not notice any blood or wound at first so i thought nothing of it. I do not how i missed it. I then eat tuna and took out ice cream sandwich which was in a small box ( containing 5 individual sandwiches wrapped individually in foil-like paper). I was holding the wrapper and eating the ice cream in the hand which had the wound. Only after I eat it i noticed the bleeding (a lot) , washed my hand and put a bandage on. 
Now...what if the ice cream wrapper was touched by someone who also had a cut and his/her blood got blood on it ( during manufacture) . I know it is very, very far fetched but could you please entertain the idea? Ice cream was transported frozen. Would his/her blood survive on the wrapper of the ice cream sandwich (in the box, closely packaged with other 4 ice cream sandwiches? The ice cream was made about 4,5 months ago. Thanks and please forgive my stupid thoughts. I just know HIV blood survives when frozen, so I am worried thinking it is far fetched, but would it still be possible to get sick if that happened or the virus would not survive for some reason despite the temperature? Thanks again. 
PS I saw someone asked about blood IN ice cream earlier, but i thought maybe mine is different + i had a very fresh, bleeding wound. 

PPS It looked like if blood was there, it would be tightly touching the wrapper of the other one as in the box sandwiches are stacked very closely (like slices of bread)  , so no much air would be there "touching" the blood. Thank you  

Welcome to the forum. Thanks for your question.---

Thank you so much, Doctor! Last related question and we can close this after your answer. In a very, very , very unlikely scenario that when a worker was handling the ice cream and his/her blood got on the wrapper (I saw on youtube they put wrapped ice cream into those small boxes manually without wearing gloves) and that contaminated wrapper touched my wound 4 months later, eventhough the ice cream was transported in freezing temperature, the virus still would not survive to be infectious, correct? The reason I got a bit paranoid is because I saw blood on the wrapper after i noticed my cut which was most likely to be mine, but I still got scared. I have a little baby I am nursing, so I am worried. I had HIV tests during and after pregnancy and it was negative.  Thank you and please forgive this temporary paranoa on my part. 

Actually, HIV probably would survive the sequence of events you describe. But that's not thie issue. There probably have been billiions of exposure to live HIV in the environment (in food, in moist body fluids in toilets, on eating utensils, and other situation), but nobody has been infected through such contact. For example, the household members of persons with HIV never catch it, unless they also are sex or needle-sharing partners of the infected person -- despite years of sharing bathrooms, kitchens, food, etc.  As I said above, if there were such instances, there would be at least some HIV infected people who don't have the standard risk factors. This is why, in the earliest days of the known HIV/AIDS epidemic, health officials were able to reassure the public about lack of risk from casual contact or the environment, even before the virus causing AIDS was discovered. In fact, HIV is rather hard to transmit. (Even the regular sex partners of infected persons often go years before they become infected themselves, and many never du. The average transmission risk for unprotected vaginal sex, if one person has HIV, is once for ever 1000-2000 exposures. Given that, what can it possibly be after the sorts of contact you're asking about?)---

"Actually, HIV probably would survive the sequence of events you describe."
This got me scared a bit, but thank you for your honesty. No, I am not a germaphob, but my immunity has been down a lot after giving birth and stress, so I started, as a consequence, thinking about those issues. Now I am almost crying thinking that if HIV survived, as you say it might had (if it was even there, of course, which I am praying it was not and there was just my blood) then as my immunity is very low I may be so unlucky.  My husband died from cancer 2,5 months ago, and thinking I may deal with something like that make me very , very sad. 
I found out (a bit of internet searching) that mostly women work in that factory (300 people work there in total) and official HIV rate where the factory is located among adult population is 0.01%  . So it would be like 1 in a million chance, correct? And I should not stop nursing my baby and forget about it? Would you (honestly)? Thank you so much. I know you are limited by 3 responses, Doctor, so I shall not bother you again, I promise. Thank you

"My immunity has been down" really doesn't matter. First, all pregnancy is associated with relative immune deficiency, but that's probably recovering. And contrary to common belief, stress does not reduce immune competence. But most important, having impaired immunity rarely increases the risk of catching various infections, including HIV. Impaired immunity can make many infections worse, once they have been caught but has little or no effect at all on risk of exposure. So while colds may seem more common when people might have lower immunity, it's just that the cold symptoms are more obvious, not an increased risk of catching one.---